Bi-twisted conjugacy in finite groups
Pieter Senden, Sam Tertooy
TL;DR
This paper introduces new methods to compute bi-twisted conjugacy classes in finite groups using character theory and endomorphism analysis, establishing inequalities and relations with automorphisms.
Contribution
It presents two novel approaches for counting bi-twisted conjugacy classes and explores their connections to representation theory and fixed-point free automorphisms.
Findings
Methods to determine bi-twisted conjugacy classes via irreducible characters
Counting twisted conjugacy classes of endomorphisms
Inequalities and congruences for Reidemeister numbers
Abstract
We provide two alternative ways to determine the number of (bi-)twisted conjugacy classes in a finite group: one by counting certain irreducible characters and one by counting certain twisted conjugacy classes of other endomorphisms. In addition, we show various inequalities and congruences for Reidemeister numbers, as well as relations between bi-twisted conjugacy, representation theory, and fixed-point free automorphisms.
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Taxonomy
TopicsFinite Group Theory Research · Geometric and Algebraic Topology · Advanced Combinatorial Mathematics